International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 11, Pages 679-684
doi:10.1155/S0161171201006032
A new inequality for a polynomial
Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110025, India
Received 7 August 2000; Revised 23 October 2000
Copyright © 2001 K. K. Dewan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let p(z)=a0+∑j=tnajzj be a polynomial of degree n, having no zeros in |z|<k, k≥1 then it has been shown that for R>1 and |z|=1, |p(Rz)−p(z)|≤(Rn−1)(1+AtBtKt+1)/(1+kt+1+AtBt(kt+1+k2t))max|z|=1|p(z)|−{1−(1+AtBtkt+1)/(1+kt+1+AtBt(kt+1+k2t))}((Rn−1)m/kn), where m=min|z|=k|p(z)|, 1≤t<n, At=(Rt−1)/(Rn−1), and Bt=|at/a0|. Our result generalizes and improves some
well-known results.